Finite Group Databasebeta

← C2×#13082475 #15661844

Subgroups — C2×#13082475 #15661844

Order 2816.

7130 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082475C2132yesmaximal, direct product factor
2C2×#10623195C212yesmaximal, complemented
3C2×#10623216C212yesmaximal, complemented
4C2×#10623172C211yesmaximal, characteristic, complemented
5C2×#10623064C211yesmaximal, characteristic, complemented
6C2×#10623064C212yesmaximal, complemented
7C2×#10623233C212yesmaximal, complemented
8C2×#10623166C211yesmaximal, characteristic, complemented
9C2×#10623042C211yesmaximal, characteristic, complemented
10C2×#10623112C211yesmaximal, characteristic, complemented
11C2×#10623072C211yesmaximal, characteristic, complemented
12C2×#10623225C211yesmaximal, characteristic, complemented
13C2×#10623223C212yesmaximal, complemented
14C2×#10623191C212yesmaximal, complemented
15C2×#10623159C211yesmaximal, characteristic, complemented
16C2×#10623159C211yesmaximal, characteristic, complemented
17C2×#10623219C211yesmaximal, characteristic, complemented
18C2×#10623079C211yesmaximal, characteristic
19C2×#10623237C212yesmaximal, complemented
20C2×#10623059C212yesmaximal, complemented
21C2×#10623035C211yesmaximal, characteristic, complemented
22C2×#10623054C211yesmaximal, characteristic, complemented
23C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
24C2×C11×#552C211yesmaximal, characteristic, complemented
25C22×Q8×D11C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C22×#4339C2211yescharacteristic
28C11×#552C22116yescomplemented
29C2×C11×#126C2212yes—
30C2×C11×#125C2211yescharacteristic
31C2×C11×#125C2212yes—
32C2×C11×#123C2212yes—
33C2×C11×C22⋊Q8C2211yescharacteristic
34C2×C11×C22⋊Q8C2211yescharacteristic
35C2×C4×Q8×C11C2211yescharacteristic
36C2×C4×D4×C11C2211yescharacteristic
37C2×C11×#117C2212yes—
38C2×C11×#117C2211yescharacteristic
39C22×C11×C4⋊C4C2211yescharacteristic
40C2×#66999C2211yescharacteristic
41C2×#66999C2211yescharacteristic
42C2×Q8×Dic11C2211yescharacteristic
43C2×#66993C2211yescharacteristic
44C2×#66991C2211yescharacteristic
45C2×#66988C2212yes—
46C2×C4×C22⋊D11C2212yes—
47C2×C4×C22⋊D11C2212yes—
48C2×C4×C22⋊D11C2211yescharacteristic
49C2×C4×C22⋊D11C2211yescharacteristic
50C2×C4×C22⋊D11C2212yes—
51C2×#66979C2211yescharacteristic
52C22×C4⋊Dic11C2211yescharacteristic
53C2×#66977C2211yescharacteristic
54C2×#66977C2211yescharacteristic
55C2×#66977C2212yes—
56#10623237C22132yescomplemented
57#10623233C22132yescomplemented
58#10623225C22116yescomplemented
59#10623223C22132yescomplemented
60#10623219C22116yescomplemented
61#10623216C22132yescomplemented
62#10623195C22132yescomplemented
63#10623191C22132yescomplemented
64#10623172C22116yescomplemented
65#10623166C22116yescomplemented
66#10623159C22116yescomplemented
67#10623159C22116yescomplemented
68#10623112C22116yescomplemented
69C4×Q8×D11C22116yescomplemented
70#10623079C22116yes—
71#10623072C22116yescomplemented
72#10623064C22132yescomplemented
73#10623064C22116yescomplemented
74#10623059C22132yescomplemented
75#10623054C22116yescomplemented
76C2×#66951C2212yes—
77C2×#66951C2212yes—
78#10623042C22116yescomplemented
79C2×#66950C2211yescharacteristic
80C2×#66950C2211yescharacteristic
81C2×#66950C2212yes—
82C2×#66949C2212yes—
83C2×#66949C2212yes—
84C2×#66949C2212yes—
85C2×#66948C2211yescharacteristic
86C2×#66947C2212yes—
87C2×#66947C2212yes—
88C2×#66947C2212yes—
89C2×#66947C2212yes—
90#10623035C22116yescomplemented
91C2×#66946C2212yes—
92C2×#66945C2212yes—
93C2×#66945C2211yescharacteristic
94C2×#66945C2211yescharacteristic
95C2×#66945C2211yescharacteristic
96C2×#66945C2211yescharacteristic
97C2×C4⋊C4×D11C2211yescharacteristic
98C2×C4⋊C4×D11C2211yescharacteristic
99C2×C4⋊C4×D11C2212yes—
100C2×C4⋊C4×D11C2211yescharacteristic
101C2×#66943C2212yes—
102C2×#66942C2212yes—
103C2×#66942C2212yes—
104C2×#66942C2212yes—
105C2×#66942C2212yes—
106C2×#66941C2211yescharacteristic
107C2×#66941C2211yescharacteristic
108C2×#66941C2212yes—
109C2×#66941C2211yescharacteristic
110C2×#66941C2212yes—
111C2×#66940C2212yes—
112C2×#66940C2211yescharacteristic
113C2×#66940C2212yes—
114C2×#66940C2212yes—
115C2×#66940C2212yes—
116C2×#66940C2212yes—
117C2×#66938C2212yes—
118C2×#66938C2212yes—
119C2×#66938C2211yescharacteristic
120C2×#66938C2211yescharacteristic
121C2×#66938C2212yes—
122C2×#66938C2212yes—
123C2×#66937C2211yescharacteristic
124C2×#66937C2211yescharacteristic
125C2×#66936C2212yes—
126C2×#66936C2212yes—
127C2×(C22⋊D11)⋊C4C2212yes—
128C2×(C22⋊D11)⋊C4C2212yes—
129C2×(C22⋊D11)⋊C4C2212yes—
130C2×#66932C2212yes—
131C2×#66932C2212yes—
132C2×#66932C2212yes—
133C2×#66931C2212yes—
134C2×#66930C2212yes—
135C2×#66929C2212yes—
136C2×#66929C2212yes—
137C2×C4×D44C2211yescharacteristic
138C2×C4×D44C2212yes—
139C2×#66925C2212yes—
140C2×C42×D11C2212yes—
141C2×C42×D11C2211yescharacteristic
142C2×#66923C2211yescharacteristic
143C2×C4×Dic22C2211yescharacteristic
144C2×C4×Dic22C2212yes—
145C2×C4×Dic22C2212yes—
146C2×C4×Dic22C2212yes—
147C22×Q8×C11C2311yescharacteristic
148C22×D4×C11C2311yescharacteristic
149C23×C4×C11C2311yescharacteristic
150C23×C4×C11C2311yescharacteristic
151C23×C4×C11C2312yes—
152C22×C22⋊D11C2311yescharacteristic
153C22×C22⋊D11C2311yescharacteristic
154C22×C22⋊D11C2311yescharacteristic
155C22×C22⋊D11C2311yescharacteristic
156C22×C22⋊D11C2311yescharacteristic
157C22×C22⋊D11C2311yescharacteristic
158C23×Dic11C2312yes—
159C2×Q8×D11—28no—
160C2×Q8×D11C2318yes—
161C2×#4339—28no—
162C2×#4339—28no—
163C2×#4339C2318yes—
164C2×#4339C2318yes—
165C22×D44C2311yescharacteristic
166C22×D44C2311yescharacteristic
167C22×D44C2311yescharacteristic
168C22×C4×D11C2311yescharacteristic
169C22×C4×D11C2312yes—
170C22×C4×D11C2311yescharacteristic
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2312yes—
173C22×C4×D11C2311yescharacteristic
174C22×C4×D11C2312yes—
175C22×C4×D11C2312yes—
176C22×C4×D11C2311yescharacteristic
177C22×Dic22C2311yescharacteristic
178C22×Dic22C2312yes—
179C22×Dic22C2312yes—
180C22×Dic22C2311yescharacteristic
181C22×Dic22C2311yescharacteristic
182C22×Dic22C2312yes—
183C11×#126C23116yes—
184C11×#125C23116yes—
185C11×#125C2318yes—
186C11×#123C23116yes—
187C11×C22⋊Q8C2318yes—
188C11×C22⋊Q8C2318yes—
189C4×Q8×C11C2318yes—
190C4×D4×C11C2318yes—
191C11×#117C2318yes—
192C11×#117C23116yes—
193C2×C11×C4⋊C4C2312yes—
194C2×C11×C4⋊C4C2312yes—
195C2×C11×C4⋊C4C2312yes—
196C2×C11×C4⋊C4C2312yes—
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2312yes—
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2312yes—
201C2×C11×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2318yes—
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2312yes—
208C2×C11×C22⋊C4C2312yes—
209C2×C42×C11C2312yes—
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2312yes—
212C2×C22⋊Dic11C2312yes—
213C2×C22⋊Dic11C2311yescharacteristic
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2312yes—
216C2×C22⋊Dic11C2312yes—
217#66999C2318yes—
218#66999C2318yes—
219Q8×Dic11C2318yes—
220#66993C2318yes—
221#66991C2318yes—
222#66988C23116yes—
223C4×C22⋊D11C23116yes—
224C4×C22⋊D11C23116yes—
225C4×C22⋊D11C23116yes—
226C4×C22⋊D11C2318yes—
227C4×C22⋊D11C2318yes—
228C2×(C2×D11)⋊C4C2311yescharacteristic
229C2×(C2×D11)⋊C4C2312yes—
230C2×(C2×D11)⋊C4C2311yescharacteristic
231C2×(C2×D11)⋊C4C2312yes—
232C2×(C2×D11)⋊C4C2312yes—
233C2×(C2×D11)⋊C4C2312yes—
234C2×(C2×D11)⋊C4C2311yescharacteristic
235C2×(C2×D11)⋊C4C2312yes—
236C2×(C2×D11)⋊C4C2312yes—
237C2×(C2×D11)⋊C4C2312yes—
238C2×(C2×D11)⋊C4C2312yes—
239C2×(C2×D11)⋊C4C2311yescharacteristic
240#66979C2318yes—
241C2×C4⋊Dic11C2312yes—
242C2×C4⋊Dic11C2312yes—
243C2×C4⋊Dic11C2312yes—
244C2×C4⋊Dic11C2311yescharacteristic
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248C2×C4⋊Dic11C2312yes—
249C2×C4⋊Dic11C2318yes—
250#66977C23116yes—
251#66977C2318yes—
252#66977C2318yes—
253C2×Dic11⋊C4C2312yes—
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2312yes—
256C2×Dic11⋊C4C2312yes—
257C2×Dic11⋊C4C2312yes—
258C2×Dic11⋊C4C2312yes—
259C2×Dic11⋊C4C2312yes—
260C2×Dic11⋊C4C2312yes—
261C2×Dic11⋊C4C2312yes—
262C2×Dic11⋊C4C2312yes—
263C2×Dic11⋊C4C2312yes—
264C2×Dic11⋊C4C2312yes—
265C2×Dic11⋊C4C2312yes—
266C2×Dic11⋊C4C2312yes—
267C2×Dic11⋊C4C2311yescharacteristic
268C2×C4×Dic11C2312yes—
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2312yes—
271C2×C4×Dic11C2312yes—
272C2×C4×Dic11C2312yes—
273C2×C4×Dic11C2312yes—
274C2×C4×Dic11C2312yes—
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2312yes—
278C2×C4×Dic11C2312yes—
279#66951C23116yes—
280#66951C23116yes—
281#66950C2318yes—
282#66950C2318yes—
283#66950C23116yes—
284#66949C23116yes—
285#66949C23116yes—
286#66949C23116yes—
287#66948C2318yes—
288#66947C23116yes—
289#66947C23116yes—
290#66947C23116yes—
291#66947C23116yes—
292#66946C23116yes—
293#66945C23116yes—
294#66945C2318yes—
295#66945C2318yes—
296#66945C2318yes—
297#66945C2318yes—
298C4⋊C4×D11C2318yes—
299C4⋊C4×D11C2318yes—
300C4⋊C4×D11C2318yes—
301C4⋊C4×D11C23116yes—
302#66943C23116yes—
303#66942C23116yes—
304#66942C23116yes—
305#66942C23116yes—
306#66942C23116yes—
307#66941C23116yes—
308#66941C2318yes—
309#66941C23116yes—
310#66941C2318yes—
311#66941C2318yes—
312#66940C23116yes—
313#66940C23116yes—
314#66940C23116yes—
315#66940C2318yes—
316#66940C23116yes—
317#66940C23116yes—
318#66938C2318yes—
319#66938C23116yes—
320#66938C23116yes—
321#66938C23116yes—
322#66938C2318yes—
323#66938C23116yes—
324#66937C2318yes—
325#66937C2318yes—
326#66936C23116yes—
327#66936C23116yes—
328(C22⋊D11)⋊C4C23116yes—
329(C22⋊D11)⋊C4C23116yes—
330(C22⋊D11)⋊C4C23116yes—
331#66932C23116yes—
332#66932C23116yes—
333#66932C23116yes—
334#66931C23116yes—
335#66930C23116yes—
336#66929C23116yes—
337#66929C23116yes—
338C4×D44C23116yes—
339C4×D44C2318yes—
340#66925C23116yes—
341C42×D11C23116yes—
342C42×D11C2318yes—
343#66923C2318yes—
344C4×Dic22C23116yes—
345C4×Dic22C23116yes—
346C4×Dic22C23116yes—
347C4×Dic22C2318yes—
348C2×#3507—111nomaximal, Sylow
349C24×C11C2411yescharacteristic
350C24×C11C2411yescharacteristic
351C23×D11C2411yescharacteristic
352C23×D11C2411yescharacteristic
353C23×D11C2411yescharacteristic
354C2×Q8×C11—24no—
355C2×Q8×C11C2414yes—
356C2×D4×C11—42no—
357C2×D4×C11C2414yes—
358C22×C4×C11—24no—
359C22×C4×C11—24no—
360C22×C4×C11—44no—
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2412yes—
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2412yes—
367C22×C4×C11C2412yes—
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2414yes—
370C22×C4×C11C2414yes—
371C22×C4×C11C2418yes—
372C22×C4×C11C2411yescharacteristic
373C2×C22⋊D11—24no—
374C2×C22⋊D11—24no—
375C2×C22⋊D11—24no—
376C2×C22⋊D11—24no—
377C2×C22⋊D11—24no—
378C2×C22⋊D11—24no—
379C2×C22⋊D11C2414yes—
380C2×C22⋊D11C2414yes—
381C2×C22⋊D11C2414yes—
382C2×C22⋊D11C2414yes—
383C2×C22⋊D11C2414yes—
384C2×C22⋊D11C2414yes—
385C22×Dic11—44no—
386C22×Dic11C2412yes—
387C22×Dic11C2412yes—
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C22×Dic11C2412yes—
391C22×Dic11C2411yescharacteristic
392C22×Dic11C2412yes—
393C22×Dic11C2418yes—
394C22×Dic11C2411yescharacteristic
395C22×Dic11C2411yescharacteristic
396Q8×D11—232no—
397#4339—232no—
398#4339—232no—
399C2×D44—24no—
400C2×D44—24no—
401C2×D44—42no—
402C2×D44C2414yes—
403C2×D44C2414yes—
404C2×D44C2414yes—
405C2×C4×D11—24no—
406C2×C4×D11—28no—
407C2×C4×D11—24no—
408C2×C4×D11—24no—
409C2×C4×D11—44no—
410C2×C4×D11—44no—
411C2×C4×D11—44no—
412C2×C4×D11—42no—
413C2×C4×D11#4118yes—
414C2×C4×D11C2414yes—
415C2×C4×D11C2418yes—
416C2×C4×D11C2414yes—
417C2×C4×D11C2414yes—
418C2×C4×D11C2418yes—
419C2×C4×D11C2414yes—
420C2×C4×D11C2418yes—
421C2×C4×D11C2418yes—
422C2×C4×D11C2414yes—
423C2×Dic22—24no—
424C2×Dic22—24no—
425C2×Dic22—28no—
426C2×Dic22—28no—
427C2×Dic22—24no—
428C2×Dic22—44no—
429C2×Dic22C2414yes—
430C2×Dic22C2418yes—
431C2×Dic22C2418yes—
432C2×Dic22C2414yes—
433C2×Dic22C2414yes—
434C2×Dic22C2418yes—
435C11×C4⋊C4C2418yes—
436C11×C4⋊C4C2418yes—
437C11×C4⋊C4C2418yes—
438C11×C4⋊C4C2418yes—
439C11×C4⋊C4C2414yes—
440C11×C4⋊C4C2418yes—
441C11×C4⋊C4C2414yes—
442C11×C4⋊C4C2418yes—
443C11×C4⋊C4C2414yes—
444C11×C4⋊C4C2414yes—
445C11×C22⋊C4C2414yes—
446C11×C22⋊C4C2418yes—
447C11×C22⋊C4C2414yes—
448C11×C22⋊C4C2418yes—
449C11×C22⋊C4C2418yes—
450C42×C11C2418yes—
451C42×C11C2414yes—
452C42×C11C2418yes—
453C22⋊Dic11C2418yes—
454C22⋊Dic11C2414yes—
455C22⋊Dic11C2414yes—
456C22⋊Dic11C2418yes—
457C22⋊Dic11C2418yes—
458(C2×D11)⋊C4C2414yes—
459(C2×D11)⋊C4C2418yes—
460(C2×D11)⋊C4C2414yes—
461(C2×D11)⋊C4C2418yes—
462(C2×D11)⋊C4C2418yes—
463(C2×D11)⋊C4C2418yes—
464(C2×D11)⋊C4C2414yes—
465(C2×D11)⋊C4C2418yes—
466(C2×D11)⋊C4C2418yes—
467(C2×D11)⋊C4C2418yes—
468(C2×D11)⋊C4C2418yes—
469(C2×D11)⋊C4C2414yes—
470C4⋊Dic11C2418yes—
471C4⋊Dic11C2418yes—
472C4⋊Dic11C2418yes—
473C4⋊Dic11C2414yes—
474C4⋊Dic11C2414yes—
475C4⋊Dic11C2414yes—
476C4⋊Dic11C2414yes—
477C4⋊Dic11C2418yes—
478Dic11⋊C4C2418yes—
479Dic11⋊C4C2414yes—
480Dic11⋊C4C2418yes—
481Dic11⋊C4C2418yes—
482Dic11⋊C4C2418yes—
483Dic11⋊C4C2418yes—
484Dic11⋊C4C2418yes—
485Dic11⋊C4C2418yes—
486Dic11⋊C4C2418yes—
487Dic11⋊C4C2418yes—
488Dic11⋊C4C2418yes—
489Dic11⋊C4C2418yes—
490Dic11⋊C4C2418yes—
491Dic11⋊C4C2418yes—
492Dic11⋊C4C2414yes—
493C4×Dic11C2418yes—
494C4×Dic11C2414yes—
495C4×Dic11C2418yes—
496C4×Dic11C2418yes—
497C4×Dic11C2418yes—
498C4×Dic11C2418yes—
499C4×Dic11C2418yes—
500C4×Dic11C2414yes—
501C4×Dic11C2414yes—
502C4×Dic11C2418yes—
503C4×Dic11C2418yes—
504#3507—1132no—
505C2×#559—112no—
506C2×#557—112no—
507C2×#556—112no—
508C2×#556—111no—
509C2×#556—111no—
510C2×#556—112no—
511C2×#554—111no—
512C2×#554—111no—
513C2×#552—111no—
514C2×#552—111no—
515C2×#552—111no—
516C2×#552D1111yescharacteristic, complemented
517C2×#539—112no—
518C2×#539—112no—
519C2×#536—111no—
520C2×#536—111no—
521C2×#533—111no—
522C2×#532—111no—
523C2×#529—112no—
524C2×#529—112no—
525C2×#520—111no—
526C2×#520—111no—
527C22×C4×Q8—111no—
528C23×C11—22no—
529C23×C11—22no—
530C23×C11—22no—
531C23×C11—22no—
532C23×C11—22no—
533C23×C11—22no—
534C23×C11C2512yes—
535C23×C11C2512yes—
536C23×C11C2511yescharacteristic
537C22×D11—22no—
538C22×D11—22no—
539C22×D11—22no—
540C22×D11—22no—
541C22×D11—22no—
542C22×D11—22no—
543C22×D11—22no—
544C22×D11—22no—
545C22×D11C2×#4114yes—
546C22×D11C2512yes—
547C22×D11C2512yes—
548C22×D11C2512yes—
549Q8×C11—28no—
550D4×C11—44no—
551C2×C4×C11—24no—
552C2×C4×C11—22no—
553C2×C4×C11—22no—
554C2×C4×C11—24no—
555C2×C4×C11—22no—
556C2×C4×C11—24no—
557C2×C4×C11—24no—
558C2×C4×C11—22no—
559C2×C4×C11—28no—
560C2×C4×C11—28no—
561C2×C4×C11—48no—
562C2×C4×C11C2×#4114yes—
563C2×C4×C11C2512yes—
564C2×C4×C11C2514yes—
565C2×C4×C11C2512yes—
566C2×C4×C11C2514yes—
567C2×C4×C11C2512yes—
568C2×C4×C11C2514yes—
569C2×C4×C11C2514yes—
570C2×C4×C11C2512yes—
571C2×C4×C11C2512yes—
572C22⋊D11—28no—
573C22⋊D11—28no—
574C22⋊D11—28no—
575C22⋊D11—28no—
576C22⋊D11—28no—
577C22⋊D11—28no—
578C2×Dic11—24no—
579C2×Dic11—22no—
580C2×Dic11—22no—
581C2×Dic11—24no—
582C2×Dic11—22no—
583C2×Dic11—24no—
584C2×Dic11—24no—
585C2×Dic11—48no—
586C2×Dic11C2×#4114yes—
587C2×Dic112−1+414yes—
588C2×Dic11C2514yes—
589C2×Dic11C2514yes—
590C2×Dic11C2512yes—
591C2×Dic11C2512yes—
592C2×Dic11C2514yes—
593C2×Dic11C2512yes—
594C2×Dic11C2514yes—
595C2×Dic11C2512yes—
596C2×Dic11C2512yes—
597D44—28no—
598D44—28no—
599D44—44no—
600C4×D11—216no—
601C4×D11—28no—
602C4×D11—28no—
603C4×D11—28no—
604C4×D11—44no—
605C4×D11—48no—
606C4×D11—48no—
607C4×D11—48no—
608C4×D11C2×#41116yes—
609Dic22—28no—
610Dic22—28no—
611Dic22—28no—
612Dic22—216no—
613Dic22—216no—
614Dic22—48no—
615C22×#41—111no—
616C22×#41—111no—
617C23×Q8—111no—
618#559—1132no—
619#557—1132no—
620#556—1132no—
621#556—1116no—
622#556—1116no—
623#556—1132no—
624#554—1116no—
625#554—1116no—
626#552—1116no—
627#552—1116no—
628#552—1116no—
629#552C2×D11116yescomplemented
630#539—1132no—
631#539—1132no—
632#536—1116no—
633#536—1116no—
634#533—1116no—
635#532—1116no—
636C2×C4⋊Q8—111no—
637C2×C4⋊Q8—111no—
638C2×C4⋊Q8—111no—
639C2×C4⋊Q8—112no—
640C2×C4⋊Q8—112no—
641C2×#127—111no—
642#529—1132no—
643#529—1132no—
644C2×#126—112no—
645C2×#126—112no—
646C2×#126—112no—
647C2×#126—112no—
648C2×#126—112no—
649C2×#126—112no—
650C2×#126—112no—
651C2×#126C2×D1112yes—
652C2×#125—112no—
653C2×#125—112no—
654C2×#125—112no—
655C2×#125—112no—
656C2×#125—112no—
657C2×#125—111no—
658C2×#125C2×D1111yescharacteristic
659C2×#125C2×D1112yes—
660C2×#124—112no—
661C2×#124—112no—
662C2×#124—111no—
663C2×#124—111no—
664C2×#124—112no—
665C2×#124—112no—
666C2×#123—112no—
667C2×#123—112no—
668C2×#123—112no—
669C2×#123—112no—
670C2×#123—112no—
671C2×#123—112no—
672C2×#123—112no—
673C2×#123C2×D1112yes—
674C2×C22⋊Q8—111no—
675C2×C22⋊Q8—111no—
676C2×C22⋊Q8—111no—
677C2×C22⋊Q8—111no—
678C2×C22⋊Q8—112no—
679C2×C22⋊Q8—112no—
680C2×C22⋊Q8—112no—
681C2×C22⋊Q8—112no—
682C2×C22⋊Q8—111no—
683C2×C22⋊Q8—111no—
684C2×C22⋊Q8—112no—
685C2×C22⋊Q8—112no—
686C2×C22⋊Q8C2×D1111yescharacteristic
687C2×C22⋊Q8C2×D1111yescharacteristic
688C2×#121—111no—
689C2×#121—111no—
690C2×#121—111no—
691C2×#121—111no—
692#520—1116no—
693#520—1116no—
694C2×C4×Q8—111no—
695C2×C4×Q8—1116no—
696C2×C4×Q8—111no—
697C2×C4×Q8—112no—
698C2×C4×Q8—112no—
699C2×C4×Q8—112no—
700C2×C4×Q8—112no—
701C2×C4×Q8—112no—
702C2×C4×Q8—111no—
703C2×C4×Q8—112no—
704C2×C4×Q8—112no—
705C2×C4×Q8—112no—
706C2×C4×Q8C2×D1111yescharacteristic
707C2×C4×D4—112no—
708C2×C4×D4—112no—
709C2×C4×D4—112no—
710C2×C4×D4—111no—
711C2×C4×D4—111no—
712C2×C4×D4—112no—
713C2×C4×D4—112no—
714C2×C4×D4—112no—
715C2×C4×D4—112no—
716C2×C4×D4—112no—
717C2×C4×D4—111no—
718C2×C4×D4C2×D1111yescharacteristic
719C2×#117—111no—
720C2×#117—111no—
721C2×#117—111no—
722C2×#117—111no—
723C2×#117—111no—
724C2×#117—112no—
725C2×#117—112no—
726C2×#117—112no—
727C2×#117C2×D1111yescharacteristic
728C2×#117C2×D1112yes—
729C22×C4⋊C4—111no—
730C22×C4⋊C4—111no—
731C22×C4⋊C4—112no—
732C22×C4⋊C4—111no—
733C22×C4⋊C4—111no—
734C22×C4⋊C4C2×D1111yescharacteristic
735C22×C42—112no—
736C22×C42—111no—
737C22×C11—22no—
738C22×C11—22no—
739C22×C11—22no—
740C22×C11—22no—
741C22×C11—22no—
742C22×C11—22no—
743C22×C11—44no—
744C22×C11—44no—
745C22×C11C22×#4112yes—
746C22×C11C2×2−1+412yes—
747C22×C11#58512yes—
748C22×C11C2611yescharacteristic
749C2×D11—22no—
750C2×D11—22no—
751C2×D11—28no—
752C2×D11—22no—
753C2×D11—22no—
754C2×D11—22no—
755C2×D11—22no—
756C2×D11—22no—
757C2×D11—22no—
758C2×D11—44no—
759C2×D11—44no—
760C2×D11C22×#4114yes—
761C4×C11—22no—
762C4×C11—22no—
763C4×C11—24no—
764C4×C11—24no—
765C4×C11—22no—
766C4×C11—24no—
767C4×C11—24no—
768C4×C11—22no—
769C4×C11C22×#4114yes—
770Dic11—24no—
771Dic11—22no—
772Dic11—22no—
773Dic11—24no—
774Dic11—22no—
775Dic11—24no—
776Dic11—24no—
777Dic11C22×#4114yes—
778Dic11C2×2−1+414yes—
779C2×#41—118no—
780C2×#41—118no—
781C2×#41—228no—
782C2×#41—228no—
783C22×Q8—118no—
784C22×Q8—112no—
785C22×Q8—111no—
786C22×Q8—112no—
787C22×Q8—111no—
788C22×Q8—111no—
789C22×Q8—112no—
790C22×Q8—228no—
791C22×Q8C22×D1111yescharacteristic
792C22×D4—111no—
793C22×D4—111no—
794C22×D4—111no—
795C22×D4—111no—
796C22×D4—111no—
797C22×D4—111no—
798C22×D4—111no—
799C22×D4—111no—
800C22×D4—111no—
801C22×D4C22×D1111yescharacteristic
802C23×C4—111no—
803C23×C4—112no—
804C23×C4—111no—
805C23×C4—111no—
806C23×C4—112no—
807C23×C4—111no—
808C23×C4—112no—
809C23×C4—111no—
810C23×C4—112no—
811C23×C4—112no—
812C23×C4C22×D1111yescharacteristic
813C23×C4C22×D1111yescharacteristic
814C23×C4C22×D1112yes—
815C4⋊Q8—118no—
816C4⋊Q8—118no—
817C4⋊Q8—118no—
818C4⋊Q8—1116no—
819C4⋊Q8—1116no—
820#127—118no—
821#126—1116no—
822#126—1116no—
823#126—1116no—
824#126—1116no—
825#126—1116no—
826#126—1116no—
827#126—1116no—
828#126C22×D11116yes—
829#125—1116no—
830#125—1116no—
831#125—1116no—
832#125—1116no—
833#125—1116no—
834#125—118no—
835#125C22×D1118yes—
836#125C22×D11116yes—
837#124—1116no—
838#124—1116no—
839#124—118no—
840#124—118no—
841#124—1116no—
842#124—1116no—
843#123—1116no—
844#123—1116no—
845#123—1116no—
846#123—1116no—
847#123—1116no—
848#123—1116no—
849#123—1116no—
850#123C22×D11116yes—
851C22⋊Q8—118no—
852C22⋊Q8—118no—
853C22⋊Q8—118no—
854C22⋊Q8—118no—
855C22⋊Q8—1116no—
856C22⋊Q8—1116no—
857C22⋊Q8—1116no—
858C22⋊Q8—118no—
859C22⋊Q8—118no—
860C22⋊Q8—1116no—
861C22⋊Q8—1116no—
862C22⋊Q8—1116no—
863C22⋊Q8C22×D1118yes—
864C22⋊Q8C22×D1118yes—
865#121—118no—
866#121—118no—
867#121—118no—
868#121—118no—
869C4×Q8—118no—
870C4×Q8—118no—
871C4×Q8—1116no—
872C4×Q8—1116no—
873C4×Q8—1116no—
874C4×Q8—1116no—
875C4×Q8—1116no—
876C4×Q8—118no—
877C4×Q8—1116no—
878C4×Q8—1116no—
879C4×Q8—1116no—
880C4×Q8C22×D1118yes—
881C4×D4—1116no—
882C4×D4—1116no—
883C4×D4—1116no—
884C4×D4—118no—
885C4×D4—118no—
886C4×D4—1116no—
887C4×D4—1116no—
888C4×D4—1116no—
889C4×D4—1116no—
890C4×D4—1116no—
891C4×D4—118no—
892C4×D4C22×D1118yes—
893#117—118no—
894#117—118no—
895#117—118no—
896#117—118no—
897#117—118no—
898#117—1116no—
899#117—1116no—
900#117—1116no—
901#117C22×D1118yes—
902#117C22×D11116yes—
903C2×C4⋊C4—111no—
904C2×C4⋊C4—111no—
905C2×C4⋊C4—112no—
906C2×C4⋊C4—112no—
907C2×C4⋊C4—112no—
908C2×C4⋊C4—112no—
909C2×C4⋊C4—112no—
910C2×C4⋊C4—112no—
911C2×C4⋊C4—112no—
912C2×C4⋊C4—118no—
913C2×C4⋊C4—111no—
914C2×C4⋊C4—112no—
915C2×C4⋊C4—112no—
916C2×C4⋊C4—112no—
917C2×C4⋊C4—112no—
918C2×C4⋊C4—112no—
919C2×C4⋊C4—111no—
920C2×C4⋊C4—111no—
921C2×C4⋊C4—111no—
922C2×C4⋊C4—112no—
923C2×C4⋊C4—112no—
924C2×C4⋊C4—112no—
925C2×C4⋊C4—112no—
926C2×C4⋊C4—112no—
927C2×C4⋊C4—118no—
928C2×C4⋊C4—1116no—
929C2×C4⋊C4—118no—
930C2×C4⋊C4—118no—
931C2×C4⋊C4C22×D1111yescharacteristic
932C2×C4⋊C4C22×D1111yescharacteristic
933C2×C4⋊C4C22×D1112yes—
934C2×C4⋊C4C22×D1112yes—
935C2×C4⋊C4C22×D1118yes—
936C2×C4⋊C4C22×D1111yescharacteristic
937C2×C4⋊C4C22×D1112yes—
938C2×C4⋊C4C22×D1112yes—
939C2×C4⋊C4C22×D1111yescharacteristic
940C2×C4⋊C4C22×D1112yes—
941C2×C4⋊C4C22×D1112yes—
942C2×C22⋊C4—112no—
943C2×C22⋊C4—112no—
944C2×C22⋊C4—111no—
945C2×C22⋊C4—111no—
946C2×C22⋊C4—112no—
947C2×C22⋊C4—111no—
948C2×C22⋊C4—111no—
949C2×C22⋊C4—112no—
950C2×C22⋊C4—112no—
951C2×C22⋊C4—112no—
952C2×C22⋊C4—112no—
953C2×C22⋊C4—112no—
954C2×C22⋊C4—112no—
955C2×C22⋊C4—111no—
956C2×C22⋊C4—111no—
957C2×C22⋊C4—112no—
958C2×C22⋊C4—112no—
959C2×C22⋊C4C22×D1111yescharacteristic
960C2×C22⋊C4C22×D1111yescharacteristic
961C2×C22⋊C4C22×D1112yes—
962C2×C22⋊C4C22×D1112yes—
963C2×C22⋊C4C22×D1112yes—
964C2×C42—112no—
965C2×C42—112no—
966C2×C42—112no—
967C2×C42—112no—
968C2×C42—112no—
969C2×C42—112no—
970C2×C42—111no—
971C2×C42—112no—
972C2×C42—112no—
973C2×C42—111no—
974C2×C42—111no—
975C2×C42—1116no—
976C2×C42—118no—
977C2×C42C22×D1112yes—
978C2×C42C22×D1112yes—
979C2×C42C22×D1111yescharacteristic
980C2×C11—42no—
981C2×C11—42no—
982C2×C11#350714yescomplemented
983C2×C11C23×#4111yescharacteristic
984C2×C11C22×2−1+411yescharacteristic
985C2×C11C2×#58511yescharacteristic
986D11—24no—
987D11—42no—
988D11—42no—
989C24—111no—
990C24—111no—
991C24—111no—
992C24C23×D1111yescharacteristic
993C24C23×D1111yescharacteristic
994#41—2232no—
995#41—2232no—
996C2×Q8—24no—
997C2×Q8—118no—
998C2×Q8—114no—
999C2×Q8—118no—
1000C2×Q8—114no—
1001C2×Q8—114no—
1002C2×Q8—118no—
1003C2×Q8—228no—
1004C2×Q8—224no—
1005C2×Q8—224no—
1006C2×Q8—228no—
1007C2×Q8—2232no—
1008C2×Q8—224no—
1009C2×Q8—444no—
1010C2×Q8C23×D1114yes—
1011C2×D4—42no—
1012C2×D4—114no—
1013C2×D4—114no—
1014C2×D4—114no—
1015C2×D4—114no—
1016C2×D4—114no—
1017C2×D4—114no—
1018C2×D4—114no—
1019C2×D4—114no—
1020C2×D4—114no—
1021C2×D4—224no—
1022C2×D4—224no—
1023C2×D4—224no—
1024C2×D4—224no—
1025C2×D4—224no—
1026C2×D4—224no—
1027C2×D4—224no—
1028C2×D4—224no—
1029C2×D4—442no—
1030C2×D4C23×D1114yes—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—44no—
1034C22×C4—111no—
1035C22×C4—111no—
1036C22×C4—118no—
1037C22×C4—114no—
1038C22×C4—112no—
1039C22×C4—112no—
1040C22×C4—112no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—112no—
1045C22×C4—118no—
1046C22×C4—114no—
1047C22×C4—118no—
1048C22×C4—114no—
1049C22×C4—114no—
1050C22×C4—118no—
1051C22×C4—114no—
1052C22×C4—118no—
1053C22×C4—118no—
1054C22×C4—224no—
1055C22×C4—228no—
1056C22×C4—224no—
1057C22×C4—224no—
1058C22×C4—444no—
1059C22×C4—444no—
1060C22×C4—444no—
1061C22×C4—442no—
1062C22×C4—444no—
1063C22×C4C23×D1114yes—
1064C22×C4C23×D1114yes—
1065C22×C4C23×D1111yescharacteristic
1066C22×C4C23×D1112yes—
1067C22×C4C23×D1112yes—
1068C22×C4C23×D1111yescharacteristic
1069C22×C4C23×D1112yes—
1070C22×C4C23×D1111yescharacteristic
1071C22×C4C23×D1112yes—
1072C22×C4C23×D1111yescharacteristic
1073C22×C4C23×D1118yes—
1074C22×C4C23×D1111yescharacteristic
1075C4⋊C4—114no—
1076C4⋊C4—114no—
1077C4⋊C4—118no—
1078C4⋊C4—118no—
1079C4⋊C4—118no—
1080C4⋊C4—118no—
1081C4⋊C4—118no—
1082C4⋊C4—118no—
1083C4⋊C4—118no—
1084C4⋊C4—114no—
1085C4⋊C4—118no—
1086C4⋊C4—118no—
1087C4⋊C4—118no—
1088C4⋊C4—118no—
1089C4⋊C4—118no—
1090C4⋊C4—114no—
1091C4⋊C4—114no—
1092C4⋊C4—114no—
1093C4⋊C4—118no—
1094C4⋊C4—118no—
1095C4⋊C4—118no—
1096C4⋊C4—118no—
1097C4⋊C4—118no—
1098C4⋊C4C23×D1114yes—
1099C4⋊C4C23×D1114yes—
1100C4⋊C4C23×D1118yes—
1101C4⋊C4C23×D1118yes—
1102C4⋊C4C23×D1114yes—
1103C4⋊C4C23×D1118yes—
1104C4⋊C4C23×D1118yes—
1105C4⋊C4C23×D1114yes—
1106C4⋊C4C23×D1118yes—
1107C4⋊C4C23×D1118yes—
1108C22⋊C4—118no—
1109C22⋊C4—118no—
1110C22⋊C4—114no—
1111C22⋊C4—114no—
1112C22⋊C4—118no—
1113C22⋊C4—114no—
1114C22⋊C4—114no—
1115C22⋊C4—118no—
1116C22⋊C4—118no—
1117C22⋊C4—118no—
1118C22⋊C4—118no—
1119C22⋊C4—118no—
1120C22⋊C4—118no—
1121C22⋊C4—114no—
1122C22⋊C4—114no—
1123C22⋊C4—118no—
1124C22⋊C4—118no—
1125C22⋊C4C23×D1114yes—
1126C22⋊C4C23×D1114yes—
1127C22⋊C4C23×D1118yes—
1128C22⋊C4C23×D1118yes—
1129C22⋊C4C23×D1118yes—
1130C42—118no—
1131C42—114no—
1132C42—118no—
1133C42—118no—
1134C42—114no—
1135C42—114no—
1136C42—118no—
1137C42—118no—
1138C42—118no—
1139C42—118no—
1140C42—118no—
1141C42C23×D1118yes—
1142C42C23×D1114yes—
1143C42C23×D1118yes—
1144C11C2×#350711yescharacteristic, complemented, Sylow
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—114no—
1152C23—112no—
1153C23—112no—
1154C23—112no—
1155C23—222no—
1156C23—222no—
1157C23—222no—
1158C23—222no—
1159C23—222no—
1160C23—222no—
1161C23—222no—
1162C23—222no—
1163C23C24×D1112yes—
1164C23C24×D1112yes—
1165C23C24×D1111yescharacteristic
1166Q8—28no—
1167Q8—2216no—
1168Q8—228no—
1169Q8—228no—
1170Q8—2216no—
1171Q8—228no—
1172Q8—448no—
1173D4—44no—
1174D4—228no—
1175D4—228no—
1176D4—228no—
1177D4—228no—
1178D4—228no—
1179D4—228no—
1180D4—228no—
1181D4—228no—
1182D4—444no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—28no—
1192C2×C4—28no—
1193C2×C4—48no—
1194C2×C4—114no—
1195C2×C4—114no—
1196C2×C4—112no—
1197C2×C4—112no—
1198C2×C4—1116no—
1199C2×C4—114no—
1200C2×C4—114no—
1201C2×C4—114no—
1202C2×C4—112no—
1203C2×C4—112no—
1204C2×C4—112no—
1205C2×C4—114no—
1206C2×C4—228no—
1207C2×C4—2216no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—224no—
1211C2×C4—224no—
1212C2×C4—224no—
1213C2×C4—222no—
1214C2×C4—224no—
1215C2×C4—228no—
1216C2×C4—228no—
1217C2×C4—448no—
1218C2×C4—448no—
1219C2×C4—448no—
1220C2×C4—444no—
1221C2×C4—448no—
1222C2×C4#41×D1114yes—
1223C2×C4C24×D1112yes—
1224C2×C4C24×D1114yes—
1225C2×C4C24×D1114yes—
1226C2×C4C24×D1112yes—
1227C2×C4C24×D1114yes—
1228C2×C4C24×D1112yes—
1229C2×C4C24×D1114yes—
1230C2×C4C24×D1112yes—
1231C2×C4C24×D1112yes—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—44no—
1239C22—44no—
1240C22—114no—
1241C22—222no—
1242C22—222no—
1243C22—228no—
1244C22—222no—
1245C22—222no—
1246C22—222no—
1247C22—222no—
1248C22—222no—
1249C22—222no—
1250C22—444no—
1251C22—444no—
1252C22C2×#41×D1112yes—
1253C22#1062345312yes—
1254C22D11×2−1+412yes—
1255C22C25×D1111yescharacteristic
1256C4—22no—
1257C4—22no—
1258C4—24no—
1259C4—22no—
1260C4—24no—
1261C4—24no—
1262C4—24no—
1263C4—22no—
1264C4—114no—
1265C4—114no—
1266C4—222no—
1267C4—222no—
1268C4—224no—
1269C4—224no—
1270C4—224no—
1271C4—224no—
1272C4—222no—
1273C4C2×#41×D1114yes—
1274C2—42no—
1275C2—42no—
1276C2—224no—
1277C2—442no—
1278C2—442no—
1279C2#1308247514yesdirect product factor
1280C2C22×#41×D1111yescharacteristic
1281C2C2×D11×2−1+411yescharacteristic
1282C2C2×#1062345311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#552C2
socleC23×C11C25
prime radicalC2×#10623079C2
hypercenterC2×#552D11
hypocenterC11C2×#3507
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#552

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082475C2direct (N × H)
2. C2×#10623195C2semidirect
3. C2×#10623216C2semidirect
4. C2×#10623172C2semidirect
5. C2×#10623064C2semidirect
6. C2×#10623064C2semidirect
7. C2×#10623233C2semidirect
8. C2×#10623166C2semidirect
9. C2×#10623042C2semidirect
10. C2×#10623112C2semidirect
11. C2×#10623072C2semidirect
12. C2×#10623225C2semidirect
13. C2×#10623223C2semidirect
14. C2×#10623191C2semidirect
15. C2×#10623159C2semidirect
16. C2×#10623159C2semidirect
17. C2×#10623219C2semidirect
19. C2×#10623237C2semidirect
20. C2×#10623059C2semidirect
21. C2×#10623035C2semidirect
22. C2×#10623054C2semidirect
23. C2×C4×Q8×D11C2semidirect
24. C2×C11×#552C2semidirect
28. C11×#552C22semidirect
56. #10623237C22semidirect
57. #10623233C22semidirect
58. #10623225C22semidirect
59. #10623223C22semidirect
60. #10623219C22semidirect
61. #10623216C22semidirect
62. #10623195C22semidirect
63. #10623191C22semidirect
64. #10623172C22semidirect
65. #10623166C22semidirect
66. #10623159C22semidirect
67. #10623159C22semidirect
68. #10623112C22semidirect
69. C4×Q8×D11C22semidirect
71. #10623072C22semidirect
72. #10623064C22semidirect
73. #10623064C22semidirect
74. #10623059C22semidirect
75. #10623054C22semidirect
78. #10623042C22semidirect
90. #10623035C22semidirect
516. C2×#552D11semidirect
629. #552C2×D11semidirect
982. C2×C11#3507semidirect
1144. C11C2×#3507semidirect
1279. C2#13082475direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130824752
C2×#106231952
C2×#106232162
C2×#106231722
C2×#106230642
C2×#106232332
C2×#106231662
C2×#106230422
C2×#106231122
C2×#106230722
C2×#106232252
C2×#106232232
C2×#106231912
C2×#106231592
C2×#106232192
C2×#106230792
C2×#106232372
C2×#106230592
C2×#106230352
C2×#106230542
C2×C4×Q8×D112
C2×C11×#5522
C2×#350711